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        <h2>
          <span class="refentrytitle">GEN14</span>
        </h2>
        <p>GEN14 — 
      Stores a polynomial whose coefficients derive from Chebyshevs of the second kind.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp214364224"></a>
        <h2>Description</h2>
        <p>
      Uses Chebyshev coefficients to generate stored polynomial functions which, under waveshaping, can be used to split a sinusoid into harmonic partials having a pre-definable spectrum.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp214408528"></a>
        <h2>Syntax</h2>
        <pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 14 xint xamp h0 h1 h2 ...</pre>
      </div>
      <div class="refsect1">
        <a id="idp214410592"></a>
        <h2>Initialization</h2>
        <p>
      <span class="emphasis"><em>size</em></span> -- number of points in the table. Must be a power of 2 or a power-of-2 plus 1 (see <a class="link" href="f.html" title="f Statement (or Function Table Statement)"><em class="citetitle">f statement</em></a>). The normal value is power-of-2 plus 1.
    </p>
        <p>
      <span class="emphasis"><em>xint</em></span> -- provides the left and right values [<span class="emphasis"><em>-xint, +xint</em></span>] of the x interval over which the polynomial is to be drawn. These subroutines both call <a class="link" href="GEN03.html" title="GEN03"><em class="citetitle">GEN03</em></a> to draw their functions; the p5 value here is therefore expanded to a negative-positive p5, p6 pair before <span class="emphasis"><em>GEN03</em></span> is actually called. The normal value is 1.
    </p>
        <p>
      <span class="emphasis"><em>xamp </em></span> -- amplitude scaling factor of the sinusoid input that is expected to produce the following spectrum.
    </p>
        <p>
      <span class="emphasis"><em>h0, h1, h2,</em></span> etc. -- relative strength of partials 0 (DC), 1 (fundamental), 2 ... that will result when a sinusoid of amplitude

      </p>
        <div class="literallayout">
          <p><br />
xamp * int(size/2)/xint<br />
      </p>
        </div>
        <p>

      is waveshaped using this function table. These values thus describe a frequency spectrum associated with a particular factor <span class="emphasis"><em>xamp</em></span> of the input signal.
    </p>
        <div class="note" style="margin-left: 0.5in; margin-right: 0.5in;">
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              </td>
              <th align="left">Note</th>
            </tr>
            <tr>
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                <p>
        </p>
                <div class="itemizedlist">
                  <ul class="itemizedlist" style="list-style-type: disc; ">
                    <li class="listitem">
                      <p>
              <a class="link" href="GEN13.html" title="GEN13"><em class="citetitle">GEN13</em></a> is the function generator normally employed in standard waveshaping. It stores a polynomial whose coefficients derive from the Chebyshev polynomials of the first kind, so that a driving sinusoid of strength <span class="emphasis"><em>xamp</em></span> will exhibit the specified spectrum at output. Note that the evolution of this spectrum is generally not linear with varying <span class="emphasis"><em>xamp</em></span>. However, it is bandlimited (the only partials to appear will be those specified at generation time); and the partials will tend to occur and to develop in ascending order (the lower partials dominating at low <span class="emphasis"><em>xamp</em></span>, and the spectral richness increasing for higher values of <span class="emphasis"><em>xamp</em></span>). A negative <span class="emphasis"><em>hn</em></span> value implies a 180 degree phase shift of that partial; the requested full-amplitude spectrum will not be affected by this shift, although the evolution of several of its component partials may be. The pattern +,+,-,-,+,+,... for <span class="emphasis"><em>h0,h1,h2..</em></span>. will minimize the normalization problem for low <span class="emphasis"><em>xamp</em></span> values (see above), but does not necessarily provide the smoothest pattern of evolution.
            </p>
                    </li>
                    <li class="listitem">
                      <p>
              <span class="emphasis"><em>GEN14</em></span> stores a polynomial whose coefficients derive from Chebyshevs of the second kind.
            </p>
                    </li>
                  </ul>
                </div>
                <p>
      </p>
              </td>
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      <div class="refsect1">
        <a id="idp214428864"></a>
        <h2>Examples</h2>
        <p>
      Here is an example of the GEN14 opcode. It uses the file <a class="ulink" href="examples/gen14.csd" target="_top"><em class="citetitle">gen14.csd</em></a>.
           </p>
        <div class="example">
          <a id="idp214430736"></a>
          <p class="title">
            <strong>Example 1104. Example of the GEN14 opcode.</strong>
          </p>
          <div class="example-contents">
            <p>See the sections <a class="link" href="UsingRealTime.html" title="Real-Time Audio"><em class="citetitle">Real-time Audio</em></a> and <a class="link" href="CommandFlags.html" title="Csound command line"><em class="citetitle">Command Line Flags</em></a> for more information on using command line flags.</p>
            <pre class="programlisting">
<span class="csdtag">&lt;CsoundSynthesizer&gt;</span>
<span class="csdtag">&lt;CsOptions&gt;</span>
<span class="comment">; Select audio/midi flags here according to platform</span>
-odac  <span class="comment">;;;realtime audio out</span>
<span class="comment">;-iadc    ;;;uncomment -iadc if realtime audio input is needed too</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o gen14.wav -W ;;; for file output any platform</span>
<span class="csdtag">&lt;/CsOptions&gt;</span>
<span class="csdtag">&lt;CsInstruments&gt;</span>

<span class="ohdr">sr</span> <span class="op">=</span> 44100 
<span class="ohdr">ksmps</span> <span class="op">=</span> 32 
<span class="ohdr">nchnls</span> <span class="op">=</span> 2 
<span class="ohdr">0dbfs</span>  <span class="op">=</span> 1 
<span class="comment">;after the example from The Csound Book, page 83</span>

<span class="oblock">instr</span> 1	<span class="comment">;compare results from GEN13 &amp; GEN14</span>
		
iwshpfn	<span class="op">=</span> p6	
inrmfn	<span class="op">=</span> p7	
aswp	<span class="opc">linseg</span>	0.01, p3<span class="op">*</span>.5, .49, p3<span class="op">*</span>.5, 0.01		<span class="comment">;index sweep function</span>
aindex	<span class="opc">poscil</span>	aswp, p5, 2				<span class="comment">;sound to waveshape</span>
atable	<span class="opc">tablei</span>	aindex, iwshpfn, 1, .5			<span class="comment">;waveshape index</span>
anrm	<span class="opc">tablei</span>	aswp<span class="op">*</span>2, inrmfn, 1			<span class="comment">;normalization </span>
aenv	<span class="opc">linen</span>	p4, .01, p3, .02			<span class="comment">;amplitude envelope</span>
asig	<span class="op">=</span> (atable<span class="op">*</span>anrm)<span class="op">*</span>aenv				<span class="comment">;normalize and impose envelope</span>
asig    <span class="opc">dcblock2</span> asig					<span class="comment">;get rid of DC</span>
	<span class="opc">outs</span>    asig, asig

<span class="oblock">endin</span>		
<span class="csdtag">&lt;/CsInstruments&gt;</span>
<span class="csdtag">&lt;CsScore&gt;</span>

<span class="stamnt">f</span> 2 0 8192 10 1			<span class="comment">;sine wave</span>

<span class="stamnt">f</span> 28  0   4097 13  1 1 1 0 .8 0 .5 0 .2		<span class="comment">;waveshaping function: GEN13 - odd harmonics</span>
<span class="stamnt">f</span> 280 0   2049 4   28 1				<span class="comment">;normalization function for f28</span>
<span class="stamnt">f</span> 29  0   4097 14  1 1 1 0 .8 0 .5 0 .2		<span class="comment">;waveshaping function: GEN14 - same harmonics</span>
<span class="stamnt">f</span> 290 0   2049 4   29 1				<span class="comment">;normalization function for f29</span>


<span class="stamnt">f</span> 30  0   4097 13  1 1 0 1 0 .6 0 .4 0 .1	<span class="comment">;waveshaping function: GEN13 - even harmonics</span>
<span class="stamnt">f</span> 301 0   2049 4   30 1				<span class="comment">;normalization function for f30</span>
<span class="stamnt">f</span> 31  0   4097 14  1 1 0 1 0 .6 0 .4 0 .1	<span class="comment">;waveshaping function: GEN13 - even harmonics</span>
<span class="stamnt">f</span> 310 0   2049 4   31 1				<span class="comment">;normalization function for 31</span>
<span class="stamnt">s</span>
<span class="stamnt">i</span>1 0   3   .7   440 28  280 
<span class="stamnt">i</span>1 4   .   .7    .  29  290
<span class="stamnt">i</span>1 8   .   .7    .  30  301
<span class="stamnt">i</span>1 12  3   .7    .  31  310

<span class="stamnt">e</span>
<span class="csdtag">&lt;/CsScore&gt;</span>
<span class="csdtag">&lt;/CsoundSynthesizer&gt;</span>
</pre>
          </div>
        </div>
        <p><br class="example-break" />  
        <span class="phrase">These are the diagrams of the waveforms of the GEN14 routines, as used in the example:</span>

      </p>
        <div class="mediaobject">
          <img src="images/gen14_1.png" alt="f28 0 4097 13 1 1 1 0 .8 0 .5 0 .2 - waveshaping function: GEN13, odd harmonics" />
          <div class="caption">
            <p>f28 0 4097 13  1 1 1 0 .8 0 .5 0 .2 - waveshaping function: GEN13, odd harmonics</p>
          </div>
        </div>
        <p>

      </p>
        <div class="mediaobject">
          <img src="images/gen14_2.png" alt="f29 0 4097 14 1 1 1 0 .8 0 .5 0 .2 - waveshaping function: GEN14, the same odd harmonics" />
          <div class="caption">
            <p>f29 0 4097 14  1 1 1 0 .8 0 .5 0 .2 - waveshaping function: GEN14, the same odd harmonics</p>
          </div>
        </div>
        <p>

      </p>
        <div class="mediaobject">
          <img src="images/gen14_3.png" alt="f30 0 4097 13 1 1 0 1 0 .6 0 .4 0 .1 - waveshaping function: GEN13, even harmonics" />
          <div class="caption">
            <p>f30 0 4097 13  1 1 0 1 0 .6 0 .4 0 .1 - waveshaping function: GEN13, even harmonics</p>
          </div>
        </div>
        <p>

      </p>
        <div class="mediaobject">
          <img src="images/gen14_4.png" alt="f31 0 4097 14 1 1 0 1 0 .6 0 .4 0 .1 - waveshaping function: GEN14, the same even harmonics" />
          <div class="caption">
            <p>f31 0 4097 14  1 1 0 1 0 .6 0 .4 0 .1 - waveshaping function: GEN14, the same even harmonics</p>
          </div>
        </div>
        <p>

    </p>
      </div>
      <div class="refsect1">
        <a id="idp214449424"></a>
        <h2>See Also</h2>
        <p>
      <a class="link" href="GEN03.html" title="GEN03"><em class="citetitle">GEN03</em></a>,
      <a class="link" href="GEN13.html" title="GEN13"><em class="citetitle">GEN13</em></a>, and
      <a class="link" href="GEN15.html" title="GEN15"><em class="citetitle">GEN15</em></a>.
          </p>
        <p> Information about the Chebyshev polynomials on Wikipedia: <a class="ulink" href="http://en.wikipedia.org/wiki/Chebyshev_polynomials" target="_top"><em class="citetitle">http://en.wikipedia.org/wiki/Chebyshev_polynomials</em></a></p>
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